Файлы
Обратная связь
Для правообладателей
Найти
Троян В.Н. Принципы решения обратных геофизических задач
Файлы
Академическая и специальная литература
Геологические науки и горное дело
Геофизика
Теория обработки геофизических данных
Назад
Скачать
Подождите немного. Документ загружается.
s
(
t
0
)
s
(
t
0
)
=
~
ρ
T
(
t
0
)
S
(
t
0
)
~
ρ
(
t
0
)
,
~
ρ
(
t
0
)
S
(
t
0
)
=
k
S
µν
(
t
0
)
k
n
µ,ν
~
ρ
(
t
0
)
=
[
ρ
1
(
t
0
)
,
ρ
2
(
t
0
)
,
.
.
.
,
ρ
n
(
t
0
)]
,
S
µν
(
t
0
)
=
12
t
0
+
L/
2
Z
t
0
−
L/
2
ϕ
µ
(
t
)
ϕ
ν
(
t
)(
t
−
t
0
)
2
dt.
σ
2
ρ
(
t
0
)
=
h
(
h
θ
(
t
0
)
i
−
h
ˆ
θ
(
t
0
)
i
)
2
i
=
h
(
n
X
i
=1
ρ
i
(
t
0
)(
u
i
−
f
i
))
2
i
=
=
~
ρ
T
(
t
0
)
R
ε
~
ρ
(
t
0
)
.
~
ρ
(
t
0
)
s
(
t
0
)
σ
2
ρ
(
t
0
)
g
(
~
ρ
(
t
0
))
=
s
(
t
0
)
cos
θ
+
σ
2
(
t
0
)
β
sin
θ
=
~
ρ
T
(
t
0
)
G~
ρ
(
t
0
)
,
0
≤
θ
≤
π
/
2
G
=
S
cos
θ
+
β
R
ε
sin
θ
~
ρ
ˆ
~
ρ
=
arg
m in
g
(
~
ρ
(
t
0
))
~
B
T
~
ρ
(
t
0
)
=
1
,
~
B
=
k
B
ν
k
n
ν
=1
,
B
ν
=
T
Z
0
ϕ
ν
(
t
)
dt.
Φ(
~
ρ
)
=
~
ρ
T
G~
ρ
−
2
λ
(
~
ρ
T
~
B
−
1 )
,
∂
Φ
∂
ρ
s
=
0
,
s
=
1
,
2
,
.
.
.
,
S.
G~
ρ
−
λ
~
B
=
0
~
ρ
ˆ
~
ρ
=
λG
−
1
~
B
.
~
B
T
~
B
T
ˆ
~
ρ
=
λ
~
B
T
G
−
1
~
B
,
~
B
T
ˆ
~
ρ
=
1
,
λ
=
1
/
(
~
B
T
G
−
1
~
B
)
.
~
ρ
ˆ
~
ρ
=
G
−
1
~
B
/
(
~
B
T
G
−
1
~
B
)
.
~
u
=
~
f
(
~
θ
)
+
~
ε
ε
∈
N
(0
,
R
ε
)
f
(
θ
)
~
θ
l
1
(
~
u,
~
θ
)
=
1
2
(
~
u
−
~
f
(
~
θ
))
T
R
−
1
ε
(
~
u
−
~
f
(
~
θ
))
.
~
θ
(0)
l
1
(
~
θ
)
~
θ
(0)
~
θ
l
1
(
~
θ
)
≈
l
1
(
~
θ
(0)
)
+
∆
~
θ
T
~
d
−
(1
/
2)∆
~
θ
T
C
∆
~
θ
,
∆
~
θ
=
~
θ
−
~
θ
0
,
d
s
=
∂
l
1
(
~
θ
)
∂
θ
s
|
~
θ
=
~
θ
(0)
,
c
ss
′
=
−
∂
2
l
1
(
~
θ
)
∂
θ
s
∂
θ
s
′
|
~
θ
=
~
θ
(0)
.
∂
l
1
(
~
θ
)
∂
θ
s
=
0
⇒
C
∆
~
θ
=
~
d,
s
=
1
,
2
,
.
.
.
,
S.
c
ss
′
C
˜
c
(0)
ss
′
=
h
c
(0)
ss
′
i
=
h−
∂
2
l
1
(
~
θ
)
∂
θ
s
∂
θ
s
′
|
~
θ
=
~
θ
(0)
i
.
∆
ˆ
~
θ
(1)
=
[
˜
C
(0)
]
−
1
~
d
(0)
,
ˆ
~
θ
(1)
=
~
θ
(0)
+
∆
ˆ
~
θ
(1)
.
∆
ˆ
~
θ
(2)
=
[
˜
C
(1)
]
−
1
~
d
(1)
,
ˆ
~
θ
(2)
=
ˆ
~
θ
(1)
+
∆
ˆ
~
θ
(2)
,
d
(1)
s
=
∂
l
1
(
~
θ
)
∂
θ
s
|
~
θ
=
ˆ
~
θ
(1)
,
˜
c
(1)
ss
′
=
*
−
∂
2
l
1
(
~
θ
)
∂
θ
s
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(1)
+
.
n
∆
ˆ
~
θ
(
n
)
=
[
˜
C
(
n
−
1)
]
−
1
~
d
(
n
−
1)
,
ˆ
~
θ
(
n
)
=
ˆ
~
θ
(
n
−
1)
+
∆
ˆ
~
θ
(
n
)
,
d
(
n
−
1)
s
=
∂
l
1
(
~
θ
)
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
−
1)
,
˜
c
(
n
−
1)
ss
′
=
*
−
∂
2
l
1
(
~
θ
)
∂
θ
s
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(
n
−
1)
+
.
|
∆
ˆ
θ
(
n
)
s
/
ˆ
θ
(
n
)
s
|
≤
β
∼
10
−
2
÷
10
−
3
s
=
1
,
2
,
.
.
.
,
S
~
u
=
~
f
(
~
θ
)
+
~
ε
d
s
˜
c
ss
′
d
(
n
)
s
=
(
~
u
−
~
f
(
~
θ
))
T
R
−
1
ε
∂
~
f
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
)
,
˜
c
(
n
)
ss
′
=
h−
(
~
u
−
~
f
(
~
θ
))
T
R
−
1
ε
∂
2
~
f
∂
θ
s
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(
n
)
+
+
∂
~
f
T
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
)
R
−
1
ε
∂
~
f
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(
n
)
i
=
=
−
h
~
ε
T
i
|
{z
}
=0
R
−
1
ε
∂
2
~
f
∂
θ
s
∂
θ
s
′
+
∂
~
f
T
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
)
R
−
1
ε
∂
~
f
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(
n
)
=
=
∂
~
f
T
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
)
R
−
1
ε
∂
~
f
∂
θ
s
′
|
~
θ
=
ˆ
~
θ
(
n
)
.
f
k
(
~
θ
)
=
2
M
h
h
2
+
(
x
k
−
ξ
)
2
,
~
θ
=
{
M
,
h,
ξ
}
,
M
h
ξ
f
k
(
~
θ
)
f
k
(
~
θ
)
=
M
(2
h
2
−
x
2
k
)
(
x
2
k
+
h
2
)
5
/
2
,
~
θ
=
{
M
,
h
}
,
M
h
f
k
(
~
θ
)
=
M
h
(
x
2
k
+
h
2
)
3
/
2
,
~
θ
=
{
M
,
h
}
,
M
h
~
u
=
~
ϕ
(
~
θ
)
+
~
ε.
~
ϕ
(
~
θ
)
~
θ
(0)
~
ϕ
(
~
θ
)
≈
~
ϕ
(
~
θ
(0)
)
+
ψ
∆
~
θ
,
k
ψ
(0)
j
s
k
=
∂
ϕ
j
/∂
θ
s
|
~
θ
=
~
θ
0
∆
~
θ
(0)
=
~
θ
−
~
θ
(0)
.
˜
~
u
0
=
ψ
0
∆
~
θ
+
~
ε,
˜
~
u
0
=
~
u
−
~
ϕ
(
~
θ
0
)
∆
ˆ
~
θ
(1)
=
(
ψ
T
0
W
0
ψ
0
)
−
1
ψ
T
0
W
0
˜
~
u
0
,
W
0
W
0
=
(
ˆ
σ
2
ε
0
)
−
1
I
=
(
ˆ
~
ε
0
T
ˆ
~
ε
0
/
(
n
−
S
))
−
1
I
S
×
S
,
~
ε
0
=
~
u
−
ψ
0
~
θ
(0)
ˆ
~
θ
(1)
=
∆
ˆ
~
θ
(1)
+
~
θ
(0)
.
ˆ
~
θ
(2)
=
∆
ˆ
~
θ
(2)
+
ˆ
~
θ
(1)
,
∆
ˆ
~
θ
(2)
=
(
ψ
T
1
W
1
ψ
1
)
−
1
ψ
T
1
W
1
˜
~
u
1
,
˜
~
u
1
=
~
u
−
ϕ
(
ˆ
~
θ
(1)
)
,
k
ψ
(1)
j
s
k
=
∂
ϕ
j
∂
θ
s
|
~
θ
=
ˆ
~
θ
(1)
)
,
W
1
=
(
ˆ
σ
2
ε
1
)
−
1
I
=
ˆ
~
ε
1
T
ˆ
~
ε
1
n
−
S
!
−
1
I
S
×
S
,
ˆ
~
ε
1
=
~
u
−
ψ
1
ˆ
~
θ
(1)
.
n
n
−
1
ˆ
~
θ
(
n
)
=
∆
ˆ
~
θ
(
n
)
+
ˆ
~
θ
(
n
−
1)
,
∆
ˆ
~
θ
(
n
)
=
(
ψ
T
n
−
1
W
n
−
1
ψ
n
−
1
)
−
1
ψ
T
n
−
1
W
n
−
1
˜
~
u
n
−
1
,
˜
~
u
n
−
1
=
~
u
−
ϕ
(
ˆ
~
θ
(
n
−
1)
)
,
k
ψ
(
n
−
1)
j
s
k
=
∂
ϕ
j
∂
θ
s
|
~
θ
=
ˆ
~
θ
(
n
−
1)
,
W
n
−
1
=
ˆ
~
ε
n
−
1
T
ˆ
~
ε
n
−
1
n
−
S
!
−
1
I
S
×
S
,
ˆ
~
ε
n
−
1
=
~
u
−
ψ
n
−
1
ˆ
~
θ
(
n
−
1)
.
|
∆
ˆ
θ
(
n
)
s
/
ˆ
θ
(
n
)
s
|
≤
β
∼
10
−
2
÷
10
−
3
s
=
1
,
2
,
.
.
.
,
S
θ
ˆ
θ
ˆ
θ
=
ˆ
θ
(
u
1
,
u
2
,
.
.
.
,
u
n
)
.
I
β
P
(
|
ˆ
θ
−
θ
|
<
δ
)
=
β
,
I
β
=
[
ˆ
θ
−
δ,
ˆ
θ
+
δ
]
,
β
I
β
I
β
ˆ
θ
~
u
=
ψ
~
θ
+
ε
ˆ
θ
s
h
ˆ
θ
s
i
=
θ
s
R
θ
s
=
σ
2
ε
[(
ψ
T
W
ψ
)
−
1
]
ss
,
s
=
1
,
2
,
.
.
.
,
S,
W
ˆ
θ
s
−
θ
s
σ
ε
[(
ψ
T
W
ψ
)
−
1
]
1
/
2
ss
∈
N
(0
,
1)
.
χ
2
n
−
S
ˆ
~
ε
=
~
u
−
ψ
ˆ
~
θ
,
ˆ
~
ε
T
W
ˆ
~
ε
σ
2
ε
∈
χ
2
n
−
S
.
N
(0
,
1)
χ
2
t
t
n
−
s
=
ˆ
θ
s
−
θ
s
σ
ε
[(
ψ
T
W
ψ
)
−
1
]
1
/
2
(1
/σ
ε
)[
ˆ
~
ε
T
W
ˆ
~
ε/
(
n
−
S
)]
1
/
2
.
∈
St
(
t
n
−
S
)
P
[
|
t
n
−
S
|
≤
γ
]
=
β
.
ˆ
σ
ε
ˆ
σ
θ
s
ˆ
σ
ε
=
ˆ
~
ε
T
W
ˆ
~
ε
n
−
S
,
ˆ
σ
θ
s
=
ˆ
σ
ε
[(
ψ
T
W
ψ
)
−
1
]
ss
.
‹
1
2
...
6
7
8
9
10
11
12
...
19
20
›